Question: Solve for $x$ and $y$ using elimination. ${-3x-5y = -43}$ ${3x+2y = 19}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x-5y = -43}\thinspace$ to find $x$ ${-3x - 5}{(8)}{= -43}$ $-3x-40 = -43$ $-3x-40{+40} = -43{+40}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 8}$ into $\thinspace {3x+2y = 19}\thinspace$ and get the same answer for $x$ : ${3x + 2}{(8)}{= 19}$ ${x = 1}$